标题： 基于层状系统的钴磁晶各向异性计算中的微扰理论有效性 显示英文标题

标题： Validity of perturbation theory in calculations of magnetocrystalline anisotropy in Co-based layered systems

摘要： 对具有增强自旋轨道耦合（SOC）的钴薄膜和钴/铂双层中的磁晶各向异性（MCA）能的二阶微扰理论（PT）的有效性进行了检验。 与通过力定理（FT）获得的精确结果进行比较，揭示了MCA能随钴厚度变化的依赖关系存在显著差异。 对于具有强SOC的体系，PT无法正确描述MCA能的振荡，大大高估了其振幅，甚至在钴/铂双层中未能再现其特定的周期性。 这些失败特别涉及由钴层中在布里渊区中心（BZ）简并的量子阱（QW）少数自旋d态对产生的2单层周期的主要振荡。 这种状态的简化模型表明，PT与FT预测之间出现大差异的原因是，在BZ中心附近区域，每个对内的状态能量间隔相对于SOC强度较小，导致PT失效。 使用FT计算的MCA能振荡幅度受到连续QW对之间有限能量间隔的限制，而在PT计算中，该振幅则随着SOC强度的增加呈二次方增长。 此外，对于弱和中等SOC强度，PT的准确性随着SOC常数与温度之比的增加而降低。 这解释了为什么即使在具有相对较弱名义SOC的钴薄膜中，PT在低温下也会高估MCA能振荡的幅度。 对于钴/铂双层，PT方法中振荡幅度的强温度依赖性导致在低温和零温下的MCA能显著不同，其符号相反，且幅度比FT结果大几倍。 显示英文摘要

摘要： Validity of second-order perturbation theory (PT) is examined for magnetocrystalline anisotropy (MCA) energy in Co films with enhanced spin-orbit coupling (SOC) and Co/Pt bilayers. Comparison with accurate results obtained with the force theorem (FT) reveals significant discrepancies in the dependence of the MCA energy on the Co thickness. For systems with strong SOC, the PT fails to correctly describe the oscillations of the MCA energy, largely overestimating their amplitude and even failing (for Co/Pt bilayers) to reproduce their specific periodicity. These failures specifically concern the dominating oscillations with the 2-monolayer period which arise from pairs of quantum well (QW) minority-spin d states in the Co layer, degenerate at the centre of the Brillouin zone (BZ). A simplified model of such states demonstrates that the large discrepancies between PT and FT predictions arise from the breakdown of the PT in a region around the BZ centre where the energy spacing between states within each pair is small compared to the SOC strength. The oscillation amplitude of the MCA energy calculated with the FT is limited by the finite energy spacing between consecutive QW pairs, whereas this amplitude grows quadratically with the SOC strength in the PT calculations. Furthermore, for weak and moderate SOC strengths, the accuracy of the PT diminishes with increasing the ratio of the SOC constant to temperature. This explains why the PT overestimates the amplitude of MCA energy oscillations at low temperatures, even for the Co film with a relatively weak nominal SOC. For the Co/Pt bilayer, the strong temperature dependence of the oscillation amplitude in the PT approach leads to the MCA energies markedly different at low and zero temperatures, of opposite sign and several times larger in magnitude, compared to the FT results.